High altitude stations are often emphasized as free tropospheric
measuring sites but they remain influenced by atmospheric boundary layer
(ABL) air masses due to convective transport processes. The local and
meso-scale topographical features around the station are involved in the
convective boundary layer development and in the formation of thermally
induced winds leading to ABL air lifting. The station altitude alone is not
a sufficient parameter to characterize the ABL influence. In this study, a
topography analysis is performed allowing calculation of a newly defined
index called ABL-TopoIndex. The ABL-TopoIndex is constructed in order to
correlate with the ABL influence at the high altitude stations and long-term
aerosol time series are used to assess its validity. Topography data from
the global digital elevation model GTopo30 were used to calculate five
parameters for 43 high and 3 middle altitude stations situated on five
continents. The geometric mean of these five parameters determines a topography
based index called ABL-TopoIndex, which can be used to rank the high altitude
stations as a function of the ABL influence. To construct the ABL-TopoIndex,
we rely on the criteria that the ABL influence will be low if the station is
one of the highest points in the mountainous massif, if there is a large
altitude difference between the station and the valleys or high plains, if
the slopes around the station are steep, and finally if the inverse drainage
basin potentially reflecting the source area for thermally lifted pollutants
to reach the site is small. All stations on volcanic islands exhibit a low
ABL-TopoIndex, whereas stations in the Himalayas and the Tibetan Plateau have
high ABL-TopoIndex values. Spearman's rank correlation between aerosol
optical properties and number concentration from 28 stations and the
ABL-TopoIndex, the altitude and the latitude are used to validate this
topographical approach. Statistically significant (SS) correlations are
found between the 5th and 50th percentiles of all aerosol parameters and the
ABL-TopoIndex, whereas no SS correlation is found with the station
altitude. The diurnal cycles of aerosol parameters seem to be best explained
by the station latitude although a SS correlation is found between the
amplitude of the diurnal cycles of the absorption coefficient and the
ABL-TopoIndex.

Climate monitoring programs aim to measure climatically relevant parameters
at remote sites and to monitor rural, arctic, coastal and mountainous
environments. The majority of these programs consist of in situ instruments
probing the Atmospheric Boundary Layer (ABL). The high altitude stations
provide a unique opportunity to make long-term, continuous in situ
observations of the free troposphere (FT) with high time and space
resolution. However, it is well-known that, even if located at high altitudes,
the stations designed to measure the FT may be influenced by the transport of
boundary layer air masses. Remote sensing instruments can be used to
complement in situ measurements in order to provide more information about
the FT. For example, sun photometers measure aerosol optical depth of the
integrated atmospheric column including the FT although they don't provide
vertical information to enable separation of FT and ABL conditions. Light
detection and ranging (lidar) type instruments measure the profile of various
atmospheric parameters (meteorological, aerosol, gas-phase) and thus can
provide information not only on the ABL but also on the FT. They can be used
to detect the ABL and residual layer (RL) heights at high altitude stations
from a convenient site at lower elevation (Haeffelin et al., 2012; Ketterer
et al., 2014; Poltera et al., 2017). However, these instruments are limited in
the presence of fog and low clouds and they don't measure above the cloud
cover. Further, the use of lidar to attribute the various aerosol gradients
to ABL layers remains a complex problem. Lastly, few lidar instruments are
currently installed in regions of complex topography. Instrumented airplanes
can make detailed measurements of the vertical and spatial distribution of
atmospheric constituents and are used either during limited measurement
campaigns or on regular civil aircraft (see, e.g., the IAGOS CARIBIC
project, http://www.caribic-atmospheric.com/, last access:
20 August 2018) but because of the limited
temporal scope of most measurement campaigns, cannot provide long-term,
continuous context for the measurements. Ideally, to make FT measurements, a
combination of these techniques would be used, but due to limited resources
that is rarely possible. Thus, it is important to evaluate the constraints of
each technique. The high altitude time series from surface measurements
remain the most numerous and the longest data sets to characterize the FT and
its evolution during the last decades. Here we focus on identifying factors
controlling the influence of ABL air on high altitude surface stations hoping
to sample FT air.

The ABL is the lowest part of the atmosphere that directly interacts with the
Earth's surface and is, most of the time, structured into several sub layers.
In the case of fair-weather days, the continental ABL has a well-defined
structure and diurnal cycle leading to the development of a convective
boundary layer (CBL), also called a mixing or mixed layer, during the day and
a stable boundary layer (SBL), which is capped by a residual layer (RL) during
the night (Stull, 1988). During daytime, the aerosol concentration is maximum
in the CBL and remains high in the RL. During nighttime, the surface-emitted
species accumulate in the SBL. In the case of cloudy or rainy conditions as
well as in the case of advective weather situations, free convection is no
longer driven primarily by solar heating, but by ground thermal inertia, cold
air advection and/or cloud top radiative cooling. In those cloudy cases the
CBL development remains weaker than in the case of clear sky conditions. However long
range or RL advection can lead to a high aerosol concentration above
the CBL during daytime, leading to high altitude aerosol layers (AL) that can
be decoupled from the CBL and the SBL.

There are several rather complex mechanisms able to bring ABL air up to high
altitude (Rotach et al., 2015; Stull, 1988; De Wekker and Kossmann, 2015). An
important factor in many of these mechanisms is how the CBL develops over
mountainous massifs. In their extensive review of concepts, De Wekker and
Kossmann (2015) studied the CBL development over slope, valley, basin, and
high plains as well as over complex mountainous massifs and concluded that
the CBL height behavior can be categorized into four distinct patterns
describing their spatial extent as a function of the surface topography:
hyper-terrain following, terrain following, level and
contra-terrain following. The type of CBL height behavior depends on several
factors such as the atmospheric stability, synoptic wind speed and vertical
and horizontal scale of the orography. Stull (1992) concluded that the CBL
height tends to become more horizontal (level behavior) at the end of the
day, that deeper CBLs are less terrain following than shallower ones, and
that the CBL top is less level over orographic features with a large
horizontal extent. Even if the CBL height remains lower than the mountainous
ridges, thermally driven winds develop along slopes, or in valleys or basins
and these winds are able to bring ABL air masses up to mountainous ridges and
summits. These phenomena were extensively modeled (Gantner et al., 2003;
Zardi and Whiteman, 2012) and also measured (Gantner et al., 2003; Rotach and
Zardi, 2007; Rucker et al., 2008; Venzac et al., 2008; Whiteman et al., 2009)
and are part of the active mountainous effects allowing a vertical transport
of polluted air masses to the FT. For example, a continuous aerosol layer
(CAL) is often measured above the CBL during dry, clear-sky and convective
synoptic situations (Poltera et al., 2017). Finally, ABL air masses can also
be dynamically lifted by frontal systems, deep convections or foehn as well
as be advected from mesoscale or wider regions and influence high altitude
measurements by all these atmospheric processes.

The ABL influence of the mesoscale regions at high altitude sites were
directly shown by airborne lidar measurements over the Alps and the Apennine
(Nyeki et al., 2000, 2002; De Wekker et al., 2004) and more indirectly by the seasonal and diurnal
cycles of aerosol parameters at high altitude stations (Andrews et al.,
2011). Many methods have been used to separate FT from ABL influenced
measurements, including those based on time of day and time of year
approaches
(Baltensperger et al., 1997; Gallagher et al., 2011), wind sectors (Bodhaine
et al., 1980), the vertical component of the wind (García et al., 2014),
wind variability (Rose et al., 2017), NOx∕NOy,
NOy∕ CO ratios or radon concentrations (Griffiths et
al., 2014; Herrmann et al., 2015; Zellweger et al.,
2003) and water vapor concentrations (Ambrose et al., 2011; Obrist et al.,
2008), although none of these methods leads to an absolute screening
procedure to ensure the measurement of pure FT air masses.

Table 1List of station names, acronyms, latitude [∘], longitude
[∘], altitude [m], their mountain range or region and continent. If
aerosol time series were used, the station name is given in bold. The
references principally describe the station measurement program and,
particularly, the aerosol parameters measured.

The altitude range of stations which claim they sample in the FT (at least
some of the time) spans from about 1000 to more than 5320 m a.s.l., but a
simple analysis of the aerosol parameters (for example, the black carbon
concentration) as a function of altitude suggests that higher altitude
stations are not necessarily less influenced by anthropogenic pollution than
lower altitude sites. While station altitude may not be the main parameter
explaining the ABL influence, topographical features around the station are
nevertheless involved in the CBL development and in the formation of
thermally induced winds leading to ABL air lifting (Andrews et al., 2011;
Kleissl et al., 2007). In addition to topography there are other important
parameters determining the ABL influence at mountainous stations, such as the
wind velocity and direction, soil moisture and albedo, synoptic weather
conditions, pollution sources, and, for islands, sea surface temperature, but
none of these parameters will be considered in this study, which is solely
restricted to the analysis of the topographic influence.

The aims of this paper are twofold: (i) define a topography based index
called ABL-TopoIndex that can be utilized to rank the high altitude stations
as a function of the ABL influence and (ii) compare the potential ABL
influence of several locations in a mountainous range in order, for example,
to choose the best sampling location for accessing FT air. Some concepts
tested or used in this study are taken from the hydrology analysis field, as both air and water flow along defined, though (often) different, flow
paths. The ABL air masses flow towards high altitudes and can extend into a
three dimensional space, in contrast to the downward flow of water that can
be restricted to a two dimensional space. However, similar to hydrological
concepts, the ABL air mass reservoirs are found in the plains and valleys.

2.1 Stations

The 43 high altitude stations (Table 1 and Fig. 1) were selected based
on various criteria, such as the presence of aerosol or gaseous measurements,
their representativeness of the mountainous massif and/or the possibility of
comparing several stations from the same mountainous massif. The sites are
representative of five continents and their altitudes range between 1074 (SHN)
and 5352 m a.s.l (CHC). Note that when not specified, altitudes given in the
text correspond to altitude above sea level (a.s.l.). Even if clearly
situated within the ABL, some stations like HPB, MSY or ZEP were added to
this analysis to verify the results of the ABL-TopoIndex at lower altitude
sites. Several mountainous massifs such as the Alps, the Himalayas, the Rocky
Mountains and the Andes Cordillera are well represented with three to five
stations. Some other stations such as BEO in the Balkan Peninsula, HAC on the
Peloponnese, WLG in China, PDI in Vietnam, MKN in Kenya and the high plains
of ASK in the Hoggar Mountains of southern Algeria are the only
representative of their massif. The volcanic islands form a category in
themselves, despite being located in different oceans and at various
latitudes.

2.2 Topography data and analysis

The topography data were taken from the global digital elevation model
GTopo30 (https://lta.cr.usgs.gov/GTOPO30, last access: 20 August 2018). GTopo30 has a horizontal grid spacing of
30 arcsec corresponding to a spatial resolution between 928 m in the
East/West direction at the equator, 598 m at WHI (50∘ N) and 373 m
at the SUM polar station (72.6∘ N). In the North/South direction,
30 arcsec are almost constant with latitude and correspond to 921 m at the
equator and 931 m at the poles. The geographical coordinate system WGS84
(World Geodetic System revised in 1984) from GTopo30 was projected in the
Universal Transverse Mercator (UTM) conformal projection to ensure
homogeneity in vertical and horizontal coordinates. Due to the altitude
averaging over each grid cell, there is typically an altitude difference
between the true station altitude and its corresponding grid location. The
mean and median of the differences between the station altitude and its
representative grid point are 190 m (8.6 %) and 140 m (5.8 %). For
stations situated near the summit, the difference can be significant: five
stations have an underestimation of their altitude larger than 500 m
corresponding to 15 %–32 % (see the Supplement and particularly Table S1
for further details), despite, according to the manual, the high reported
GTOPO30 accuracy (minimum accuracy of 250 m at 90 % confidence level
with a RMSE of 152 m).

The TopoToolbox-master version of the free shareware TopoToolbox
(https://topotoolbox.wordpress.com/, last access: 20 August 2018), which is a set of matlab functions offering
analytical GIS utilities in a non-GIS environment (Schwanghart and Scherler,
2014), was used as a principal tool for the topographic relief and flow
pathways analysis in the Digital Elevation Model (DEM) analysis. The DEM were
preprocessed by filling holes with a carving process prior to calculating the
flow directions and the water flow paths were calculated with single flow
direction representation.

2.3 ABL-TopoIndex

To construct the ABL-TopoIndex, we rely on the following four criteria to
indicate that the ABL influence will be low if the following criteria are
met:

the station is one of the highest points in the mountainous massif,

there is a large altitude difference between the station and the valleys,
high plains or the average domain elevation,

the slopes around the station are steep, and

the inverse drainage basin, which potentially reflects the source area
for thermally lifted pollutants, is small.

Based on these criteria, it can be inferred from Fig. 2 that the “red”
station will be less influenced by the ABL than the “blue” station, despite
being situated at lower altitude. A quantitative estimation of these criteria
clearly depends on the domain considered. The minimal size requirement for
such a topographical analysis is that the domain should contain the whole
mountainous massif. An airborne lidar measurement of the ABL over the Alps
(Nyeki et al., 2002) clearly showed that the convective boundary layer is
formed over a large-scale and leads to an elevated and extended layer. Nyeki
et al. (2002) also quantified this “large-scale” to extend more than
200 km from the mountainous massif. A rectangular domain size of
500 km × 500 km centered on each site was thus chosen for this
analysis (see Sect. 3.2 for a discussion of the effect of the domain size).
The four criteria listed above are then represented using five parameters
(Table S2 lists topographical and hydrological parameters considered but
rejected for this analysis).

Figure 2Schematic view of the topographical features underlying the
ABL-TopoIndex.

Figure 3(a) Normalized hypsocurves for a selected subset of the high
altitude stations for a 500 km × 500 km domain centered on each station. The
filled and open circles correspond to the normalized station elevations
within the domain and indicate the value of hypso% (e.g., PYR hypso% = 26). The vertical dashed line corresponds to 50 % of the hypsometric
curve. (b) Difference between the station altitude and the elevation minimum
in a domain of radius R around the station as a function of R. The vertical
dashed line indicates the part of the curve selected to calculate LocSlope.

Parameter 1 – hypso%. A hypsometric curve is the cumulative
distribution function of elevation on the considered domain. The frequency
percentage of the hypsometric curve at the station altitude (hypso%)
provides a representation of criterion 1 for a large spatial scale
(500 km × 500 km). Figure 3a presents several normalized
hypsometric curves with dots indicating the station hypsometric value. While
most of the high altitude stations (65 %) have hypso% values less than
10 %, some stations are situated on wide inflection points of the
hypsometric curve (see, e.g., PYR and NCOS in Fig. 3a). Six stations
(see Table S1) have hypso% values larger than 50 %. BEO and FWS are
found at less than 0.1 % of the curve indicating they are located at one
of the highest points of their respective mountainous massifs. The ABL
influence should increase with increasing value of hypso%.

Parameter 2 – hypsoD50. The second parameter (hypsoD50) is the difference
between the station altitude and the altitude at 50 % of the hypsometric
curve. The median of the hypsometric curve was chosen first because a station
claiming to be a high altitude site should typically be at a higher altitude
than half of its geographical environment and, second, because the median is
a commonly used statistical concept to determine the central value of a
sample. The parameter hypsoD50 corresponds to criterion 2 for a large spatial
scale (500 km × 500 km). In some cases (see Fig. 3a and Table S1),
a station is situated under 50 % of the hypsocurve, leading to a
negative hypsoD50. For these sites the hypsoD50 is set to the very small
value of 1000/abs(hypsoD50) to allow the geometric mean to be applied (see
Eq. 1). The ABL influence should decrease with increasing values of hypsoD50.

Parameter 3 – LocSlope. The altitude difference between the station and the
minima in a circular domain centered at the station is plotted as a function
of the domain radius in Fig. 3b. The slope of this curve between 1 and 10 km
is then calculated (LocSlope) and corresponds to criteria 2 and 3 for a small
spatial scale (10 km × 10 km). The steepness of the slopes
(criterion 3) around the station is only evaluated from the station toward
the lowest elevations. The distance of 10 km to calculate the LocSlope was
chosen as representative of the maximum distance to the next adjacent level
region for almost all stations. Figure 3b shows that the change in the
altitude difference as a function of domain radius can be very different from
station to station. For example, there is a rapid decrease of the altitude
difference with increasing distance that gradually levels off for radius
larger than 7 km for JFJ and for radius larger than 4 km for MBO; there is
a continuous decrease of the altitude difference for PYR and ASK up to radius
larger than 30 km; and there are sites for which the altitude difference
stays constant for a portion of the domain radius (see for example CHC and
BEO) indicating the presence of flat terrain. NCOS appears very different
than the other sites plotted because the NCOS station is near the vast Nam
Lake (surface area 1950 km2) situated at 4718 m. The ABL influence
should increase with decreasing LocSlope.

Parameter 4 – G8. The mean gradient in elevation in the eight directions
(N, NE, E, SE, S, SW, W, NW) at the station is called G8. This parameter
takes into account the slopes towards lower and higher elevations over a
local scale (0.5–1.1 km, which is the distance between two grid cells, with
the size of the grid depending on latitude) and corresponds to criterion 3.
The ABL influence should decrease for increasing G8 gradient.

Parameter 5 – DBinv. As the air masses have to be thermally lifted from
the valleys and plains towards the summit to influence the station
measurements, the size of the inverse drainage basin (DBinv) can be
calculated with standard hydrology tools, using an inverse topography, where
the altitude Z is changed to −Z, allowing the summit to become a hole. It
potentially represents the region from which pollutants such as aerosols can
be thermally lifted without crossing any topographical barrier. DBinv is
related to criterion 4 for a large spatial scale
(500 km × 500 km). Figures 4d and 5d are examples of the DBinv
calculation for BEO and PYR. The ABL influence should increase with
increasing size of the inverse drainage basin.

Figure 4(a) Topography on a 750 × 750 km2 domain around BEO (Moussala,
white dot) in Bulgaria. The main hydrologic flow paths from the station grid
cell are given by the cyan lines. The color scale on the left only applies
to panel (a). (b) Hydrographical network and (c) hydrologic drainage basins
calculated from the real topography, the different drainage basins are
defined by various colors and (d) “inverse drainage basin” calculated from
the inverse topography (DBinv).

To summarize, the ABL influence should increase with decreasing values of
hypsoD50, LocSlope and G8 and with increasing values of hypso% and DBinv.
Thus, to determine the ABL-TopoIndex, the geometric mean is calculated on the
inverse of hypsoD50, LocSlope and G8 along with the values of hypso% and
DBinv. To avoid any particularities of the station site and due to the fact
that the ABL influence is a regional factor, the mean of the values at the
grid cell containing the station and at the eight neighboring grid cells
(recall that grid spacing is 30 arcsec) are used to calculate the
ABL-TopoIndex. The ABL-TopoIndex is then taken as the geometric mean of the
five parameters:

ABL-TopoIndex=(1)hypso%×1hypsoD50×1LocSlope×1G8×DBinv5.

The geometric mean is used here on strictly positive parameters that have
widely different numeric ranges (e.g., Table 2). The geometric mean is used
instead of the arithmetic mean because it effectively “normalizes” the
various parameter ranges, so that no parameter dominates the weighting.
Further, a given percentage change in any of the parameters will yield an
identical change in the calculated geometric mean value. In that sense, the
variability of each parameter is also normalized, leading to similar
modifications of the ABL-TopoIndex for similar parameter's variations.
Because of these properties, the geometric mean is the recommended method to
determine meaningful indices from multiple parameters (Ebert and Welsch,
2004). The extrema, median and mean of the parameters constituting the
ABL-TopoIndex are reported in Table 2. The value of the ABL-TopoIndex has no
significance in itself, so that the units are not important, but it allows
ranking of the stations as a function of the ABL influence due to convection.

2.4 Aerosol parameters

Aerosol datasets from 25 high altitude and 3 mid-altitude stations (Table 1)
were available for this study, 21 of them coming from GAW (Global Atmospheric
Watch) stations. The datasets comprise absorption coefficient, scattering
coefficient and/or number concentration and cover time periods ranging from
at least a year up to more than a decade of measurement (see
Table S3 in the Supplement). Stations with time series shorter than one year were not used,
as their data are not representative of a complete seasonal cycle. Due to
the non-normal distribution of the aerosol parameters, the 5th, 50th and 95th
percentiles were taken as representative of the minimum, central position and
maximum concentrations.

No correction for standard pressure and temperature was applied in order to
use the measured aerosol properties and concentration at high altitude. For
consistency, the measured hourly absorption and scattering coefficients were
adjusted to a wavelength of 550 nm if reported at a different wavelength
using an assumed scattering or absorption Ångström exponent of 1.
Additionally, the scattering coefficients were corrected for angular
truncation error. Due to the measurement technique and the low aerosol
concentrations at many high altitudes, filter-based photometers regularly
measure negative absorption coefficients at some of these sites. Some
datasets contain up to 20 %–30 % of negative absorption values.
Depending on the data owner's policy, these negative values were either left
in the dataset, set to zero (or to a minimum value) or considered as missing
values. To ensure a similar treatment for all datasets, negatives values,
zeros and minimum values attributed to negatives were thus set to
missing values.

Figure 5The same as Fig. 4 for PYR (Nepal Climate Observatory – Pyramid) station
in the Himalaya, Nepal.

The diurnal and seasonal cycles were only analyzed on datasets longer than
2 years. To be able to statistically calculate the diurnal and seasonal
cycles, the autocorrelations at 1 h (first lag) were first removed from
the dataset by a whitening procedure (Wang and Swail, 2001). The
autocorrelations at each lag time were then calculated on the whitened
dataset taking into account missing data (see Supplement for further
explanations). Only autocorrelation values statistically significant at
95 % confidence level were kept. As the diurnal (24 h) and annual
cycles (365 days) were not well defined due to variable meteorological
conditions and some shorter datasets, the autocorrelation at lags of 22 to 26 h
and at lags of 350 to 380 days were summed to obtain the strength (i.e., the
cycle amplitude) of the diurnal and seasonal cycles, respectively. Noise in
the aerosol measurements makes the strength of the cycle a somewhat
qualitative value. The diurnal cycles were calculated for each month of the
year in order to observe the seasonal change of the diurnal cycles.

3.1 Case studies

Mount Moussala (BEO) is the highest summit not only in Bulgaria but of the
whole Balkan massif. The regional GAW station is located at the summit
(2925 m). The topographic dominance of BEO can be visualized on the
topography map (Fig. 4a). Figure 4a also shows the main hydrological flow
paths which follow the Iskar, Martisa and Metsa rivers. Figure 4b shows the
water flow accumulations, which are the accumulated flows of all cells
flowing into each downslope cell in the output raster, allowing visualization
of the largest features of the Bulgaria hydrographic network. BEO is at the
junction of four drainage basins corresponding to the four main rivers
(Fig. 4c). Figure 4d shows that when the inverse drainage basin is calculated
with the inverse topography, BEO is in the center of a large inverse drainage
basin that covers most of the plotted domain. Even though BEO's altitude is
under 3000 m, BEO's ABL-TopoIndex of 0.52 is one of the lowest, due to an
almost zero hypso% (0.034 %), a high hypsoD50 of 2136 m and a
relatively small DBinv of 1.15×105 (Tables 2 and S2). HAC is a very similar case
to BEO as the site is situated near the top of Mount Helmos, the third
highest mountain of the Peloponnese massif in Greece.

PYR (5079 m) is the second highest station of all stations considered in
this study, but the station is located at the foot of Mount Everest (8848 m)
at a confluence point of several valleys (Fig. 5a and b). Figure 5c shows
that PYR is situated in the middle of a very large hydrological drainage
basin highlighting the fact that the PYR station is not located at a dominant
position in the Himalayas. The PYR ABL-TopoIndex is consequently quite high
(3.43) and supports the observation of a large ABL influence in the Himalayan
region (Bonasoni et al., 2008). The daily arrival of polluted air masses from
the Indo-Gangetic plain is frequently reported in PYR data analyses (Bonasoni
et al., 2010, 2012; Marinoni et al., 2010).

Figure 6(a) ABL-TopoIndex, (b) inverse drainage basin,
(c) hypsometric percentage of the station elevation,
(d) hypsometric percentage of the station elevation minus the
50 % hypsometry, (e) local slope in a circle of 10 km radius
centered on the station, (f) gradient in elevation as a function of
the domain size for some European high altitude stations.

3.2 Relation between ABL-TopoIndex and domain size

As the ABL-TopoIndex depends on the size of the chosen domain (Fig. 6a), we
have conducted an evaluation of the sensitivity of the various algorithms to
the domain size using a range from 50 to 1000 km2. The gradient criterion
G8 and the local slope criterion LocSlope are calculated on small fixed
horizontal scales (0.5–1 and 10 km, respectively) and are consequently
constant with domain size (Fig. 6e, f), although there are small fluctuations
due to some distortions occurring during the projection of GTOPO30 in the UTM
WGS84 coordinate system, primarily when the analyzed domain extends beyond
two UTM zones (see for example BEO). The other three parameters do change
with domain size which is the reason that the ABL-TopoIndex also is a
function of the domain area. DBinv tends to increase with the domain size for
all stations (Fig. 6b), as the size of the low altitude area potentially
contributing to thermally lifted pollutants increases with domain size. The
hypso% decreases continuously with domain size for stations situated in a
dominant position in their mountainous massif such as JFJ, SBO or BEO
(Fig. 6c). For stations located at a lower position in their massif (see for
example HPB), the hypso% first increases before decreasing once the domain
contains all the highest peaks of the massif. Finally, stations situated atop
a high local mountain but surrounded by higher mountains such as MUK (not
shown in Fig. 6) have a continuously increasing hypso% up to very large
domain sizes (106 km2 for MUK). HypsoD50, the difference between
the station elevation and the minimum of elevation in the domain, always
increases (or at least stays constant) with an increase in domain size but
changes more or less rapidly depending on the domain topography (Fig. 6d). In
general, the ABL-TopoIndex usually increases with an increase in domain size
(i.e., more ABL influence). The largest increases are usually found for the
stations with the highest ABL-TopoIndex at small domain sizes and are due to
an increase in DBinv overcoming the decrease in hypso% and the increase in
hypsoD50.

3.3 Relation between ABL-TopoIndex and altitude

As stated in the introduction, the development of the ABL-TopoIndex relies on
the assumption that the station position in the mountain massif is a better
criterion for determining the ABL influence than the station altitude alone.
To compare these two parameters, we show in Fig. 7 the ABL-TopoIndex as a
function of the altitude for all grid cells in a 5 km × 5 km
domain for a subset of stations. For the grid cells at the highest altitudes,
there is a clear relationship between the ABL-TopoIndex and the altitude. The
ABL-TopoIndex decreases (less ABL influence) as altitude increases. Figure 7
shows that the OMP and PYR regions have a very large ABL-TopoIndex decrease
with altitude while ASK exhibits a very small ABL-TopoIndex decrease with
altitude. At lower altitudes for each massif, the valleys, high plains and
various mountainous slopes lead to a wide range of the altitudes
corresponding to the same ABL-TopoIndex value. For example, the altitude
range corresponding to an ABL-TopoIndex of 3 varies between 3000 and 6000 m
at PYR, while at OMP an ABL-TopoIndex of 2 is achieved at an altitude range
between 250–350 m. At PYR and CHC, there are discrete groupings of points
likely corresponding to the basins of different valleys around the site. The
ABL-TopoIndex values of the stations are indicated by the square markers,
allowing visualization of their relative situation in their respective
mountain massifs: OMP, HAC and CHC and to some extent SBO were located at
places with the lowest ABL-TopoIndex of their regions thus minimizing
potential ABL influence. In contrast the region around PYR (and to a lesser
extent ASK) shows locations with much lower ABL-TopoIndex (less ABL
influence) at similar altitudes to the stations.

Figure 7ABL-TopoIndex as a function of elevation of all grid cells of a
625 km2 domain centered on the ASK, CHC, HAC, OMP, PYR and SBO
stations. The squares indicate the ABL-TopoIndex values and the altitudes of
the stations.

3.4 Relation between the ABL-TopoIndex and the station location

The ABL-TopoIndex values for the forty-six stations are grouped as shown in
Fig. 8 by continents and mountainous massifs or regions (see Table 1 and
Fig. 1) that can correspond to various geomorphologies. The first obvious
observation is that all islands have very low ABL-TopoIndex (note the
logarithmic scale for the ABL-TopoIndex), whereas the stations in the
Himalayan massif have the highest ABL-TopoIndex. The values of the
ABL-TopoIndex and of all its constituting parameters are given in Table S1.
From this, the following conclusions can be drawn.

Islands. The islands with sites included in this study have a small area, are
delimited by the large flat ocean (though most of them are grouped in
archipelagos) and their summits were formed by volcanic activity leading to
steep slopes. All these factors lead to very low ABL-TopoIndex values. The
Teide Observatory on Izaña, an island of the Canary Islands archipelago
(TDE) and Pico Mountain Observatory (OMP) in the Portuguese Azores
archipelago rank as the monitoring stations with the lowest ABL influence.
The low ABL-TopoIndex of both stations is caused by the following reasons:
(1) both mountains are the only summit of the island and the highest mountain
of their archipelago (3715 and 2350 m, respectively), (2) both islands have
small surface area (2034 and 447 km2) and (3) both research stations
are just below the mountain summits (177 and 126 m from the summit). The
effect of the proximity to the summit can be clearly seen by the difference
between TDE (ABL-TopoIndex of 0.22) and IZO (ABL-TopoIndex of 0.57). These
two sites, both located on the island of Tenerife, are separated by only
15 km in horizontal distance but a vertical distance of 1165 m, with TDE
being the higher station. Taiwan, where LLN is located, has the largest
surface area (36 193 km2) of the islands considered here and,
additionally, is in close proximity to a continent (China is 130 km to the
west). Both of these factors explain LLN's high ABL-TopoIndex in the island
category. MLO in Hawaii is at high altitude (3397 m), but the island of
Hawaii has a second summit, Mauna Kea (4205 m). Further, the MLO research
station is 870 m beneath the volcano top and has a relatively low G8,
explaining why it has a higher ABL-TopoIndex than most of the islands. This
difference in ABL-TopoIndex between OMP and MLO is confirmed by an almost
daily occurrence of buoyant upslope flow at MLO while such flow patterns are
much less frequent (<20 % of the time) at OMP (Kleissl et al., 2007).

Alps. The European Alps consist of a broad mountainous massif with the
highest summits between 4500 and 4800 m. The four high research stations
(JFJ, SBO and ZUG/ZSF) are located between 2900 and 3600 m (ZSF being only
some 300 m below ZUG). HPB (985 m) was added to this study as a low
elevation station in the Alps. All three high elevation stations have low
ABL-TopoIndex: JFJ (0.64), SBO (1.24) and ZUG (1.35). Their ABL-TopoIndex
values are generally a little higher than those determined for the islands.
As expected, the ABL influence at HPB is much stronger (ABL-TopoIndex is
5.38) due to both its lower altitude and position near the bottom of the
Zugspitze massif.

Pyrenees. The Pyrenees are a natural border between France and Spain and peak
at 3400 m. PDM is a high altitude station (2877 m) with an ABL-TopoIndex
similar to the European alpine high altitude stations. MSA is located at a
mid-altitude range of the massif and has a median ABL-TopoIndex, while the
low altitude MSY station, added for comparison purposes, has a high
ABL-TopoIndex.

Other European stations. BEO and HAC are situated at the highest points of
their massifs and thus have very low ABL-TopoIndex values, comparable
to those of the island high elevation sites. The lower altitudes of CMN and
PUY, their middle position in mountainous massifs containing several higher
summits and, to a lesser extent, their proximity to other massifs such as
the Alps and the Pyrenees result in higher ABL-TopoIndex values for these
two sites.

Figure 8ABL-TopoIndex for all stations as a function of continents and
mountain ranges. The color scheme corresponds to that in Fig. 1.

Himalayas and Tibetan Plateau. The Himalayas are the highest mountainous
massif on Earth with 14 summits peaking at more than 8000 m. The altitudes
of the research stations fall between 2200 and 5100 m but are at relatively
low elevation in comparison to the summits. This is clearly reflected in
their high ABL-TopoIndex values (between 3 and 30). MUK and SZZ are both
situated in the foothills of the Himalayas in India (Uttarakhand region) and
in south China (Yunnan region), respectively, and both have an ABL-TopoIndex
value in the 3–10 range. Although MUK is at a lower altitude than SZZ, it is
located at a higher position than SZZ relative to the mean altitude of its
meso-scale environment. The high ABL-TopoIndex values for HLE and NCOS are
due to their positions in a large valley and on the edge of a vast lake,
respectively. Such positioning largely decreases all the parameters related
to criteria 1, 2 and 3 (see Sect. 2.3). WLG is constructed within a few
meters of Mount Waliguan's summit on the northeastern part of the Tibetan
plateau; its dominant position in its meso-scale domain leads to a middle
range ABL-TopoIndex value.

Japan. Mount Fuji is the highest peak of Japan and the research station is
located at the top of the symmetric volcano located near the coast. The
second highest peak in Japan is some 500 m lower than Mount Fuji. This
particular topography leads to an ABL-TopoIndex similar to the volcanic
islands. The two other Japanese stations are at much lower altitudes and have
mid-range ABL-TopoIndex values.

North America. Mount Washington Observatory is located in the Presidential
Range of the White Mountains. It is the highest peak in the northeastern
United States and the most prominent mountain east of the Mississippi River.
MWO is consequently the North American station with the lowest ABL-TopoIndex
due to very low hypso% and relatively high G8, LocSlope and hypsoD50. Four
stations (MZW, NWR, SPL and YEL) are situated in the Rocky Mountains, whose
summits peak at 4400 m. The three stations higher than 3000 m have lower
ABL-TopoIndex values similar to some of the European mountain sites, whereas
YEL is situated on the wide Yellowstone high plains with an average elevation
of 2400 m. Thus, YEL has a high ABL-TopoIndex (7.2) that is similar to the
values for NCOS and HLE. Mount Bachelor (MBO) is located near the top of an
isolated volcano from the Cascade volcanic arc that dominates the plains
surrounding it, explaining its low ABL-TopoIndex. WHI is located in the
Pacific Coast Range, the mountain range referring to the vicinity
between the high altitude massif and the ocean coast. The highest peaks in
the Pacific Coast Range have summits between 3000 and 4000 m (WHI is at
2182 m). WHI has a middle range ABL-TopoIndex (1.4) despite its low altitude
due to the proximity of the ocean and to the rather narrow width of the
massif (300 km). APP and SHN are both situated at the same altitude in the
Blue Ridge Mountains of the Appalachian range. At the latitude of SHN, the
width of the Blue Ridge mountain range is much narrower than at APP's
latitude. Moreover SHN is almost on the top of the ridge whereas APP is on a
high plain. Therefore, SHN has higher G8 and LocSlope and lower hyps% and
DBinv, leading to much lower ABL-TopoIndex than is found for APP.

Figure 9Spearman's rank correlation coefficient characterizing the
correlation between aerosol parameters (absorption coefficient, scattering
coefficient and number concentration) and various topographic parameters (the
ABL-TopoIndex, mean altitude over the 9 grid cells, station latitude and the
five parameters constituting the ABL-TopoIndex: G8, DBinv, LocSlope, hypso%
and hypsoD50). Correlations were calculated for the 5th, 50th and 95th
percentiles of the aerosol parameters. Statistically significant correlation
values at 95 % and 90 % confidence levels are marked by large and medium
symbol sizes and the positive and negative correlations are plotted with
upward and downward triangles, respectively. The correlations were performed
with 21, 23 and 17 stations for the absorption coefficient, the scattering
coefficient and the number concentration, respectively.

Andes. CHC (5320 m), the highest station in this study, is located in the
Cordillera Oriental, itself a sub-range of the Bolivian Andes massif, and is
part of the mountain bell surrounding the Altiplano (literal translation high
plain) with an average height of 3750 m. This position explains its
mid-range ABL-TopoIndex of about 1.3 due to relatively high hypso%
(1.03 %) and low hypsoD50 (1311 m). PEV (4765 m), the South America
station with the lowest ABL-TopoIndex, is located at the extreme northeastern
extension of the South America's Andes mountain range that peaks at about
5000 m. Its high position in its mountain range is characterized by a very
low hypso% (0.28 %) and the highest hypsoD50 of 4019 m. TLL is
situated in the foothills of the Andes in Chile near to the Pacific ocean and
has a similar ABL-TopoIndex to SZZ due similarities in topography. LQO is at
higher altitude than TLL but located in the middle of the Altiplano leading
to an ABL-TopoIndex larger than 20.

Africa. Mount Kenya (5199 m), the second highest peak in Africa and the
highest in Kenya, is an isolated volcanic massif with several peaks. MKN
observatory is located some 1500 m under Mount Kenya's summit resulting in a
mid-range ABL-TopoIndex of about 1. Assekrem (ASK, 2710 m) is located on a
small (about 2.5 km2) high plain in the Hoggar Mountains located in
central Sahara. The highest summit in the Hoggar range peaks at 2908 m.
Despite being situated in a relatively flat area, ASK has quite low
ABL-TopoIndex value because of its relatively high elevation in the Hoggar
Mountains.

Arctic. SUM is located high atop the Greenland ice sheet in the central
Arctic. The ice sheet has a very smooth topography due to its build up by
glaciation and precipitation. While SUM has a high hypso%, its hypsoD50,
G8 and LocSLope are very low and its DBinv is large, leading to high
ABL-TopoIndex. The Zeppelin Observatory (475 m) in Svalbard is located near
the top of Zeppelinfjellet (556 m), above Ny-Ålesund, but cannot be
considered as a high altitude site and was added to the study for comparison
purposes. Its ABL-TopoIndex is consequently very high as the highest
summit on Spitzbergen Island is at 1717 m.

3.5 Correlation between aerosol parameters and the ABL-TopoIndex

While Fig. 8 shows that there are some clear patterns in the ABL-TopoIndex,
it is also instructive to see how the ABL-TopoIndex relates to measurements
at mountain sites. The NCOS and SUM stations have a very high ABL-TopoIndex
due to their situation on a high altitude plain near a vast lake and on the
smooth shape of the Greenland inland ice sheet, respectively. As they are
not situated in a complex topography, they were excluded from this analysis
due to their clear outlier status. ZEP, situated at very low altitude
(475 m) and very high latitude (78.9∘), also has a very high
ABL-TopoIndex value. It was also not included in the correlation analysis
as its seasonal and diurnal cycles exhibit different features than the
high altitude or middle latitude stations (see Sect. 4.1). In order to have a
robust estimate of the correlation between the aerosol measurements
(following a Johnson distribution) and the topographical parameters
(following a normal or a log-normal distribution depending on the parameter)
the Spearman's rank correlation was calculated. It should be noted that the
Kendall's tau correlation analysis leads to the same conclusions (see
Table S4). The Spearman's rank correlation measures the strength and
direction between two ranked variables without the requirement that the
variables are normally distributed. Here it is also used to verify that the
assumed relationships between topographical and aerosol parameters correspond
to those proposed in Sect. 2.3 (e.g., that a positive correlation with
aerosol loading as a surrogate for ABL influence in the case of lifting
processes without precipitation is found for the ABL-TopoIndex, hypso%,
DBinv and station altitude and an anti-correlation with aerosol loading is
found for hypsoD50, LocSlope and G8). The expected positive or negative
correlations with aerosol parameters are found for ABL-TopoIndex and all five
topographical parameters contributing to the ABL-TopoIndex. The Spearman's
rank correlation coefficients of the 5th, 50th and 95th percentiles of the
measured aerosol parameters with site altitude latitude, ABL-TopoIndex as
well as all the individual parameters constituting the ABL-TopoIndex are
presented in Fig. 9. (Similar to the ABL-TopoIndex calculation, the mean of
the altitudes of the grid cell containing the station and its eight
neighboring cells was used.)

Figure 10Spearman's rank correlation coefficient characterizing the
correlation between all the topographic parameters (see Fig. 9) and the
minimum and the maximum of the monthly diurnal cycles, as well as the
seasonal cycle of the aerosol parameters. The correlations are performed
with 21, 22 and 15 stations for the absorption coefficient, the scattering
coefficient and the number concentration, respectively.

The ABL-TopoIndex has statistically significant (SS) correlation for all of
the percentiles of all aerosol parameters except for the 95th percentile of
the scattering coefficient. The highest correlation and SS are found for
the fifth percentile of the absorption and scattering coefficient, whereas for
number concentration the ABL-TopoIndex is most highly correlated with the
50th percentile. The correlation coefficient of ABL-TopoIndex with the
maximum of the aerosol parameters (95th percentile) is always lower than with
the minimum (5th percentile) and is SS at 95 % of confidence level only
for the absorption coefficient. The fifth percentiles of the aerosol parameters, particularly of the absorption coefficient, correspond to the
measurement of air masses with the lowest aerosol concentration, namely FT
air masses with the lowest ABL influence and no advection of polluted air
masses. In contrast, the 95th percentiles correspond to the advection or
convection of air masses with high aerosol loads and can, to some extent, be
caused by special events such as dust or biomass burning events. In contrast
to the absorption coefficient, the particle number concentration (and, to a
far lower extent, the scattering coefficient) depend not only on the ABL
influence but also on the new particle formation (NPF) that can be enhanced
at high altitudes (Boulon et al., 2011; Rose et al., 2015). Thus, the high
correlation of the ABL-TopoIndex with the fifth percentile of the aerosol
absorption coefficient as well as lower correlation with the 95th percentile
of absorption coefficient, the fifth percentile of number concentration and the
95th percentile of scattering coefficient suggest the ABL-TopoIndex is indeed
a promising indicator for ABL influence based on station topography.

The hypso%, a large scale parameter, has SS correlations with all the
percentages of all the aerosol optical properties, whereas LocSlope and G8,
two small scale parameters, have SS anticorrelations except for the 95th
percentile of the scattering coefficient where no SS correlations are
observed. The hypsoD50 is SS for the 5th and 50th percentile of the
absorption and scattering coefficients and for the 50th and 95th percentile
of the number concentration. Only the DBinv exhibits no SS correlation
with any of the aerosol parameters.

There are no SS correlations between the station altitude and the
percentiles of any of the aerosol parameters. The station elevation alone is
thus not a good predictor of the ABL influence (at least as it relates
to particle concentration and aerosol optical properties). The latitude is
SS anticorrelated with the 5th and 50th percentile of the scattering
coefficient.

The correlations of the topographical parameters with the strength of the
diurnal and seasonal cycles of the aerosol measurements exhibit a different
pattern. Figure 10 shows the Spearman's rank correlation coefficients of the
topographical parameters with the minimum (Dmin) and maximum
(Dmax) strength of the monthly diurnal cycle as well as with the strength of the
seasonal cycle (Season) of the aerosol parameters. The diurnal cycles were
calculated for each of the 12 months, so that Dmin and Dmax correspond to the
lowest and the highest monthly amplitudes, respectively. For many mountain
sites, Dmin occurs when the station remains in the FT during the whole day
resulting in no systematic diurnal cycle. In contrast Dmax occurs when the
site is in the FT during the night (without any influence of the RL) and
influenced by the ABL during the day. The diurnal and the seasonal
cycles were both calculated as the strength of the autocorrelation function (see
Sect. 2.4 and Supplement) so that the underlying parameters are de facto
normalized and that the cycles of each station can be directly compared. The
highest correlation (a negative correlation) is found between the amplitudes
of the diurnal cycles and the latitude for all three aerosol parameters. This
anticorrelation is particularly noticeable for the number concentration
diurnal cycles. At low latitudes, the stronger insolation enhances the
surface temperature and the thermal convection leading to stronger diurnal
cycles, particularly in summer, while the convective flow is less likely to
be inhibited during the winter due to longer daylight hours. Together these
effects result in a larger ABL influence year round and explain the high
correlations of latitude with the diurnal cycle amplitude. The high
correlation between the maximal diurnal cycle and the number concentration
can also be explained by the promotion of NPF due to the stronger insolation
at low latitude.

The ABL-TopoIndex is SS correlated with the minimum and the maximum of the
monthly diurnal cycles of the absorption coefficient. This correlation is,
once again, primarily due to the hypso% and G8, and to a lesser extent,
the LocSlope. The highest correlation is found for the absorption
coefficient which directly depends on uplift of ABL air masses, in contrast
to the number concentration and scattering coefficient cycles which are also
influenced by gas-to-particle conversion processes such as NPF. As NPF
can be enhanced at low temperature, (i.e., NPF seasonal cycle can be
anticorrelated with the seasonality of the CBL height) the relationship
between number concentration (and, to a lesser extent, scattering) with
diurnal cycle strength may be obscured by seasonal changes in atmospheric
dynamics.

The only SS correlation with station altitude is found for the scattering
coefficient seasonal cycle. Similar to the anticorrelation of
G8 with the aerosol parameter
percentiles, there is also a high anticorrelation between the particle number
concentration diurnal cycles and G8 suggesting that the local slope steepness
inhibits both the transport of polluted air masses and NPF. Apart from a
correlation at 90 % confidence level between DBinv and the absorption
coefficient, the lack of further SS correlations for topographic parameters
with the aerosol parameter seasonal cycles can be attributed to several
factors: (i) the relatively small time period (2–5 years) covered by most of
the datasets leading to difficulties in the statistical determination of a
yearly periodicity due to inter-annual variability, (ii) the low aerosol
concentration at high altitude sites often resulting in measurements near the
detection limits of the instruments (see for example the problem with the
absorption coefficient at Sect. 2.4), (iii) the seasonal long-range transport
effects masking ABL transport and (iv) the
necessary whitening procedure (see Supplement) increasing the dataset noise.

In this section the assessments, improvements and applications of the
ABL-TopoIndex are discussed. First the possible parameters and phenomena
enabling the estimation of the ABL influence are summarized and the
occurrence of diurnal and seasonal cycles as a function of the station
elevation are discussed. Second, the significance of the correlations
between the topographical and the aerosol parameters are further
interpreted. Finally, possible additional parameters that could increase the
significance and the application of the ABL-TopoIndex are mentioned, in
addition to the criteria relevant for choosing future sites to sample FT air
masses.

4.1 Using measurements to assess the ABL influence

In order to test the relevance of the ABL-TopoIndex, it is first necessary to
find a parameter commonly measured at high altitude stations that can be used
as an ABL tracer. Pollutants emitted at the Earth's surface and having a
(typically) minimal concentration in the FT could act as potential tracers of
the ABL influence. Our results showed that of the three aerosol parameters
tested in this study (number concentration, absorption coefficient and
scattering coefficient), absorption coefficient has the highest correlation
with the ABL-TopoIndex values. Other possible candidates for testing the
ABL-TopoIndex include the aerosol mass concentration, size distribution and
chemical composition, the water vapor and the trace gases concentrations
(e.g., CO2, PAN, NOx, NOy,
O3, SO2, isotopologue ratio of water vapor) and the
radon222 concentration. These parameters have been used in different
studies to provide information about the seasonal and diurnal cycles (e.g.,
Collaud Coen et al., 2011; Griffiths et al., 2014; Marinoni et al., 2010;
McClure et al., 2016; Okamoto and Tanimoto, 2016; Pandolfi et al., 2014;
Ripoll et al., 2015; Zellweger et al., 2009), the sources and transport of
aerosol to the site (e.g., Cuevas et al., 2013; García et al., 2017;
Pandey Deolal et al., 2014; Ripoll et al., 2014), the local orographic flows
and the effect of the synoptic- and meso-scale weather types (e.g., Bonasoni
et al., 2010; Gallagher et al., 2011; González et al., 2016; Henne et
al., 2005; Kleissl et al., 2007; Tsamalis et al., 2014; Zellweger et al.,
2003). All of the extensive
aerosol parameters, the radon222, water vapor concentration, particulate
nitrate (NO3-) and organics have been shown to be correlated
with ABL transport whereas CO∕NOy and
NOx∕NOy ratios are anticorrelated
(Legreid et al., 2008; Zellweger et al., 2003). Zellweger et al. (2003)
concluded that, in contrast to NOy, the major process for
upward transport of aerosol is the thermally induced vertical transport,
confirming that the aerosol parameters used in this study could, in most
cases, be good tracers for ABL influence. However, one has to keep in mind
that many lifting processes co-occur with precipitation and, hence, potential
aerosol washout. The present validation of the ABL-TopoIndex by aerosol
measurements at high altitude stations is consequently valid only for
thermally induced processes without precipitation. ABL events involving air
masses with low aerosol concentrations due to washout – for example synoptic
lifting or foehn – were not directly analyzed.

Because there are variable pollution levels in the vicinity of the stations,
a single absolute value of a pollutant cannot be used to evaluate the
ABL-TopoIndex (or ABL influence in general) when considering multiple high
altitude stations. An inventory of the proximate pollution sources
constraining simulations with meteorological models able to explicitly
resolve the role of fine resolution orography would be required before using
absolute pollutant concentrations as indicators of ABL influence at high
altitude sites. Another possibility would be to weight the pollution source
inventories by factors depending on their vertical and horizontal distances
to the high altitude stations, as well as on a seasonal parameter
representing the potential ABL height. A further use of DBinv to restrict
the area of potential pollution sources can also be envisaged, as this
parameter describes the domain from which pollutants can reach the high
altitude station by convection without crossing topographical barriers. The
identification of pollution source areas potentially affecting the high
altitude stations can be avoided by instead considering dynamic parameters
such as the temporal cycles of various pollutants.

At most of the high altitude stations, a seasonal cycle in ABL-indicator
species is frequently observed. The maximum values of the seasonal cycles are
often correlated with ABL transport and typically occur in summer or in the
pre-monsoon season, while the minimum of the seasonal cycle occurs in winter
or monsoon seasons. Usually, at high altitude stations, the spring leads to
higher aerosol loading than the autumn; this is probably related to higher
ABL height in the spring. These seasonal cycles are explained by the stronger
thermal heating of the soil, which induces convection and buoyancy in summer
and by the atmospheric cleaning effect of precipitation during the monsoon.
It would be expected that stations continuously situated in the ABL
throughout the year could exhibit different seasonal cycles than high
altitude sites due to the seasonal modification of the sources and/or of the
synoptic and meso-scale meteorological conditions (see for example the
difference between HPB and JFJ in Fig. S2). In contrast, a station located
such that it is continuously impacted by FT air masses or with weak seasonal
cycle of the ABL influence would have a seasonal cycle that depends mostly on
long-range, high altitude transport climatology, e.g., long-range transport
of Asian dust and pollution at MLO in spring (Collaud Coen et al., 2013),
North-America ABL transport to IZO through westerlies in spring (García
et al., 2017), and dust events in EU spring and autumn (Collaud Coen et al.,
2004). As
seasonally changing parameters (e.g., temperatures, cloud cover, solar
radiation, wind speeds, surface albedo, precipitation) were not studied and
as the length of most of the time series were too short to smooth these
effects, the ABL-TopoIndex will probably not represent an overall picture of
ABL influence except at seasonally invariant sites (e.g., very low latitude
sites).

The typical diurnal cycle of ABL pollutants at high altitude stations that
are partially influenced by the ABL consists of a minimum in the early
morning (04:00–06:00 LTC) followed by an increase of the compound with a
maximum in the late afternoon (15:00–17:00 LTC) and a decrease during the
night. If the ABL influence is mostly due to orographic winds, upslope or valley
winds begin to flow some hours after sunrise and downslope or mountain winds
initiate after the occurrence of negative vertical heat flux. Stations always
situated in the FT should exhibit no systematic diurnal cycles, whereas the
stations always situated in the ABL often show various diurnal cycles that
can be explained by the behavior of local sources, the diurnal cycle of the
ABL height and/or local meteorological conditions. At high elevation and high
latitude stations the diurnal cycle typically vanishes during winter but is
clearly present during summer, spring and, to a lesser extent, autumn. For
stations at lower altitude that stay in the ABL (or CBL, SBL or RL) during
the whole day in summer (e.g., MSA, Pandolfi et al., 2013; HPB and PUY, Hervo et al., 2014), the diurnal cycle may also vanish during that period.

Testing the ABL-TopoIndex using pollutant diurnal cycles is further
complicated by the presence of the residual layer (RL) that keeps the
pollutants brought to high altitudes during the previous days at those
elevated levels during the nighttime. The climatology of the RL height
usually exhibits a similar seasonality as the ABL height, with a maximum in
summer (or pre-monsoon) season and a minimum in winter (Birmili et al., 2009,
2010; Collaud Coen et al., 2014; Wang et al., 2016). Further, the RL has a
similar dependency as the ABL on latitude, i.e., the RL's maximum height also
depends on the duration of the incoming radiation. The RL pollutant
concentrations are much higher than nighttime FT concentrations, leading to
less marked diurnal cycles in summer than in spring (Blay-Carreras et al.,
2014; Collaud Coen et al., 2011; Hallar et al., 2016; Hervo et al., 2014).
The impact of the RL on the aerosol concentration is probably one of the most
important reasons for the low correlation between the topographical
parameters and the aerosol temporal cycles. However, the statistical
determination of the diurnal and seasonal cycle amplitudes suffer from
several difficulties: (1) the low aerosol concentrations observed at high
altitude often result in measurements near the detection limit leading to
large uncertainties, (2) the high hourly autocorrelation of the data requires
a pre-whitening procedure (see Supplement) in order to be able to detect the
diurnal and seasonal cycle, (3) meteorological conditions (e.g., cloud
coverage, precipitation, seasonal fluctuations, etc.) modify the clear-sky
diurnal cycles. These factors constraining the observation of clear
statistical temporal cycles in the measurement data also contribute to the
observed low correlations between the diurnal and seasonal cycles of the
aerosol parameters and the ABL-TopoIndex.

Recently, the influences of the local and of the more regional or meso-scale
ABL at the JFJ were separated by differentiating the Local Convective
Boundary Layer (LCBL) height from the high altitude aerosol layer (Poltera et
al., 2017). The LCBL was found to rarely influence the JFJ research station
(never in winter, 4 % of the time in summer corresponding to 22 % of
the days with ABL influence), whereas the continuous aerosol layer has a
large influence on the JFJ pollutant concentrations (21 % of the time in
winter and 41 % of the time in summer corresponding to 77 % of the
days with ABL influence). This suggests that the mechanisms explaining the
heights of the LCBL and the more horizontally extended aerosol layer have
different causes and do not follow the same diurnal pattern. This phenomenon
will be more pronounced at continental high altitude stations than at marine
isolated island stations since the marine ABL is less prone to strong diurnal
cycles.

4.2 Correlation between the topography and the aerosol parameters

The correlations between topographical and aerosol parameters presented in
Sect. 3.5 can now be further discussed in light of the pollutant temporal
cycles. The absorption coefficient is primarily due to the presence of black
carbon emitted from combustion processes occurring mostly in the ABL and
rarely near the high altitude stations; additionally, BC aerosol is not
produced by any secondary processes. Among the aerosol parameters studied
here, the absorption coefficient is thus the best tracer for
anthropogenic pollution and biomass burning and consequently for ABL
influence. It is thus expected that a better correlation will be obtained
between the topography parameters increasing the ABL influence and the
absorption coefficient. The ABL-TopoIndex reflects this correspondence,
particularly through the contribution of the hypso% parameter (recall that
hypso% represents the relative altitude of a station in its mountain
range), the LocSlope and G8. The best correlation for both ABL-TopoIndex,
hypso%, Locslope and hypsoD50 are found for the fifth percentile of the
absorption coefficient, since the minima of the aerosol loading is a better
tracer of the lowest ABL influence, whereas the maxima is much more dependent
on source intensity and special events. Similar to this result, a clear
correlation was also found between the continuous aerosol layer maximum
height and the absorption coefficient measured in situ at the JFJ (Fig. 8 in
Poltera et al., 2017). The absorption coefficient amplitudes of the diurnal
cycle are also the only aerosol cycles having a SS correlation with the
ABL-TopoIndex.

It is more difficult to directly tie scattering and number concentration to
the ABL incursions. This is because the formation of new particles and their
subsequent growth are well-known to be very efficient processes at high
altitudes due to the high insolation and the low temperature. Moreover, the
NPF is also enhanced by local thermal winds and forced convection due to
favorable changes in thermodynamic conditions (Boulon et al., 2011; Rose et
al., 2015). It was found at the JFJ and confirmed at other stations that new
particle formation, and particularly strong nucleation events, occur mostly
when the air masses were in contact with the ABL within 2 days before
arriving at high altitudes (Bianchi et al., 2016). NPF and subsequent growth
of the particles have a large impact on the number concentration and its
temporal cycles and a smaller influence on the scattering coefficient. The
parameters describing the local topography (G8 and LocSlope) have the highest
correlation with the number concentration and are probably more relevant to
the local CBL transport than to the longer range continuous aerosol layer as
defined in Poltera et al. (2017). The number concentration and, to a lesser
extent, the absorption coefficient percentiles and diurnal cycles are
anti-correlated with the local (G8: 0.5–1 km) and regional (LocSlope and
hypsD50: 10 km) slopes, suggesting there is an increase of particle number
concentration when there are small altitude differences and gentle slopes
around the station. This dependence on the ease of local transport can be
explained by transport to the station not only of aerosol, but also of
gaseous precursors for NPF and of newly formed particles at lower elevations.
The higher correlation of local slope (G8 and LocSlope) with the 50th
percentile of number concentration rather than with the absorption
coefficient can be explained both by the sources of black carbon being very
few in the vicinity of most of the high altitude stations and by the smooth
pressure decrease experienced by the precursors during their upslope
transport along gentle slopes leading to more condensation processes and
nucleation.

The aerosol diurnal cycles are influenced by numerous phenomena (see
Sect. 4.1) leading to a non-trivial relationship with the ABL influence. The
study of the diurnal cycles can bring valuable results if specific cases are
analyzed and compared. The statistical approach used here is confounded to
the noise in the data (low aerosol concentration and whitening process), to
the inter-annual variability of the meteorological processes and to cloud,
precipitation and long-range advection involving a large day to day
variability. There are consequently few statistical correlations between
topography parameters and the diurnal cycles. The clearest correlation is the
influence of the insolation on the aerosol diurnal cycles amplitudes. This
dependence between the latitude and the aerosol concentration has been noted
by Kleissl et al. (2007) and is easily understandable, as the convection and
the new particle formation are directly dependent on the solar radiation
intensity. However, the other correlations found between some topography parameters
(ABL-TopoIndex, hypso%, G8 and LocSlope) and the absorption coefficient
are directly tied to the ABL influence.

4.3 Improving and applying the ABL-TopoIndex

The choice of the five parameters included in the ABL-TopoIndex was initially
based on several assumptions relating the topography to the ABL influence
(see Sect. 2.3). Several other parameters taken from the topography,
morphology or hydrology fields such as the topographical wetness index, the
upstream catchment area, the Efremov–Krcho landform classification, the
integral and index of the hypsometric curve and the topographic prominence
were tested but eliminated as being not relevant for various reasons
(Table S2). Indeed, most of the parameters comprising the ABL-TopoIndex
exhibit some correlations with aerosol parameters. The hypso%, LocSlope
and G8 are the parameters explaining the highest variance in the aerosol
optical properties, with the hypsoD50 having a lower influence than the other
three parameters. It also seems evident that the topographical parameters
linked to the steepness and the altitude differences (G8 and LocSlope) are
clear indicators for NPF. The DBinv seems to be the least explanatory
parameter in terms of ABL influence and this large scale parameter should
probably be combined with a source inventory to increase its relevance for
identifying boundary layer influence (see Sect. 4.1). However, DBinv does
have a clear influence on the statistical significance of the correlations
between the ABL-TopoIndex and the aerosol cycles (not shown in the paper) and
has the highest correlation with aerosol seasonal cycles. However, the
aerosol parameters and, particularly, the absorption coefficient cannot be
considered as unique tracers of the ABL, particularly in case of lifting
processes with precipitation. Analysis of other ABL marker (gaseous species,
radon, wind turbulence, etc.) can provide information on additional
transport mechanisms, which would allow for refinement of this topographic
analysis by adding further parameters. East-oriented slopes are heated early
during the day and thus have a larger contribution to the thermal
convection and the associated valley winds. A parameter weighting the east
slope area could thus be added to the ABL-TopoIndex. The various
geomorphologies of the mountainous ranges included in this study also raise
the question of whether the stations should all be combined together for
analysis as was done here, or if a morphological parameter should instead be
found for each massif. The mountain steepness (at larger scales than LocSlope
and G8) also determines the necessary velocity for the wind to cross the
mountains and could be an additional parameter. Finally, future studies
should attempt to build a direction dependent ABL-TopoIndex that also takes
into account the topography of each valley up to the meso-scale range.

It is important to understand the FT vs. ABL influence on historical data
sets from established high altitude observatories. The ABL-TopoIndex is one
tool that can help elucidate the different influences. A further improvement
could include an angular dependency of the ABL-TopoIndex allowing
quantification of the potential direction of the maximum ABL influence and
the pollutant sources with the largest influence. The ABL-TopoIndex may also
be useful a priori in locating measurements for a field campaign or
identifying potential sites for long-term observatories if FT measurements
are the goal, particularly when no previous measurements exist. For example,
in situ aerosol measurements are done at IZO at an altitude of 2373 m,
whereas aerosol optical depth and water vapor isotopologues measurements are
done at TDE at 3538 m on the same volcano. TDE has a much lower
ABL-TopoIndex than IZO and consequently TDE's measurements are more likely to
represent the FT. The topography around the PYR station suffers from several
factors (see Fig. 7 and Sect. 3.1) leading to a high ABL influence. Even if
the choice of the actual site is driven by compelling and practical
logistical arguments, other positions at similar altitudes in the massif
would have ensured lower pollution impact than is observed at PYR. Finally,
some stations such as BEO (2925 m), HAC (2314 m) and MWO (1916 m) are not
situated at very high altitudes but present excellent locations for FT
sampling. Obviously there are other issues to consider when deploying
instruments as well (e.g., ease of access, power availability, presence of
local pollution sources, etc.), but the ABL-TopoIndex is one factor that
could be considered to maximize the potential for FT sampling.

The ABL-TopoIndex is a topographical index based on the hypsometric curve,
the slope of the terrain around the station and the inverse drainage basin
that potentially reflects the source area for thermally lifted pollutants. It
allows one to rank the high altitude stations as a function of their ABL
influence or to optimize choice of site location for FT sampling. High
altitude stations situated on volcanic islands, the highest stations in the
Alps, in the Andes and in the Pyrenees have low ABL-TopoIndex values.
Stations situated at or near the summit of their mountainous ranges such as
BEO, HAC and MWO also have low ABL-TopoIndex values. Stations situated at
altitudes between 4000 and 5500 m in the Himalayas and the Tibetan Plateau
have high ABL-TopoIndex values due to their relatively low position compared
to the summits. Statistically significant correlations between the
ABL-TopoIndex and the aerosol parameters measured at high altitude sites
allowed validation of the methodological approach. The highest correlations
are found with the fifth percentile of the aerosol parameters representing the
minimal ABL influence or, in other words, the most likely FT air masses. The
95th percentiles of aerosol parameters are more representative of the
intensity of aerosol sources and of advection of air masses with high aerosol
concentrations. There are also strong anticorrelations between the local
steepness of the slope and the particle number concentration, suggesting that
new particle formation could be largely influenced by this topographical
parameter. If high altitude stations undergo daytime ABL air influence due to
convection, a pronounced diurnal cycle of aerosol parameters is usually
observed. The amplitude of the diurnal cycle of the absorption coefficient is
SS correlated with the ABL-TopoIndex and is thus likely to be
representative of ABL influence. However, the strength of the diurnal cycles of the
scattering coefficient and the number concentration is mostly
explained by the latitude of the station, leading to the conclusion that the
solar radiation intensity and duration drive the aerosol diurnal cycle. The
inverse drainage basin seems to be the parameter that is least explanatory in terms
of ABL influence and this large scale parameter should either be further
evaluated or be combined with a source inventory to increase its relevance
for identifying boundary layer influence.

Almost all of the data sets used for this publication are
accessible online on the WDCA (World Data Centre for Aerosols) web page:
http://ebas.nilu.no (last access: August 2018). The OMP and SBO data
will be soon accessible on the WDCA web page, but data can be also obtained
by contacting Paolo Fiahlo (fialho.paulo@gmail.com) and Gehrard Schauer
(gerhard.schauer@zamg.ac.at), respectively. PEV data will be soon be
accessible online on the Bolin Centre database
(https://bolin.su.se/data/, last access, August 2018) and can be
obtained by contacting Radovan Krejci (radovan.krejci@aces.su.se). MUK data
can be obtained by contacting Hooda Rakesh
(rakesh.k.hooda@fmi.fi).

DA, MA, HA, NB, ME, PF, HF, AGH, RH, IK, RK, NHL, AM, JM, NAN,
MP, VP, LR, SR, GS, KS, SS, JS, PT and PV contributed to the measurement of
the aerosol time series. DR was involved in several discussion concerning the
development of the ABL-TopoIndex. EA contributed to the data measurement at
some stations, to the development of the ABL-TopoIndex and to the preparation
of the manuscript. MCC developed the ABL-TopoIndex, made the correlations
between the topographical features and the aerosol parameters, prepared the
figures and wrote the manuscript.

The authors gratefully acknowledge the following persons and organizations.

Wolfgang Schwanghart, the programmer
of the TopoToolBox for putting his codes as a freeware and for all the kind
and always rapid support he offers.

CHC: the Chacaltaya consortium and Laboratory for Atmospheric Physics at
UMSA for taking care of the station and collecting the data. Swedish
participation was supported by the Swedish Foundation for International
Cooperation in Research and Higher Education (STINT) and the Swedish research
council FORMAS.

CMN: the European Commission funded ACTRIS, ACTRIS-2 EU project and NEXTDATA
National project funded by MIUR.

IZO: Global Atmospheric Watch program funded by AEMET and by the project
AEROATLAN (CGL2015-66299-P), funded by the Ministry of Economy and
Competitiveness of Spain and the European Regional Development Fund (ERDF).

JFJ: International Foundation High Altitude Research Stations Jungfraujoch
and Gornergrat (HFSJG) and the Federal Office of Meteorology and Climatology,
MeteoSwiss, within the Swiss program of the Global Atmosphere Watch (GAW) of
the World Meteorological Organization, funding from the European Union's
Horizon 2020 research and innovation programme under grant agreement no.
654109 (ACTRIS2), and the Swiss State Secretariat for Education, Research and
Innovation (SERI) under contract no. 15.0159-1. The opinions expressed and
arguments employed herein do not necessarily reflect the official views of
the Swiss Government.

LLN: the Taiwan Environmental Protection Administration.

MSA and MSY: MINECO (Spanish Ministry of Economy and Competitiveness), the
MAGRAMA (Spanish Ministry of Agriculture, Food and Environment), the
Generalitat de Catalunya (AGAUR 2014 SGR33 and the DGQA) and FEDER funds
under the PRISMA project (CGL2012-39623-C02/00). This work has received
funding from the European Union's Horizon 2020 research and innovation
programme under grant agreement No 654109. Marco Pandolfi is funded by a
Ramón y Cajal Fellowship (RYC-2013-14036) awarded by the Spanish Ministry
of Economy and Competitiveness.

MLO, NWR and SUM: the NOAA observatory staff at each station and the NOAA
Climate Program Office's Atmospheric Chemistry, Carbon Cycle and Climate
(AC4) program.

MUK: Ministry of Foreign Affairs of Finland, Academy of Finland (project
no. 264242) for the financial support and an esteemed collaboration of FMI
and TERI.

NCOS: Max Planck Institute for Chemistry and the Chinese Academy of Sciences
(Project SKLCS-ZZ-2017 and KJZD-EW-G03-03).

PDI: Federal Office of Meteorology and Climatology MeteoSwiss through the
project Capacity Building and Twinning for Climate Observing Systems (CATCOS)
Phase 2, Contract no. 81025332 between the Swiss Agency for Development and
Cooperation and MeteoSwiss.

PEV: Support from Swedish Research Council (Vetenskaprådet) and Swedish
International Development Cooperation Agency (SIDA).

PDM: Pyrenean Platform for Observation of the Atmosphere P2OA
(http://p2oa.aero.obs-mip.fr, last access: 20 August 2018), University
Paul Sabatier, Toulouse, France and CNRS (Centre National de la Recherche
Scientifique).

OMP: United States National Oceanic and Atmospheric Administration (NOAA)
grants NA16GP1658, NA86GP0325 and NA030AP430002; United States National
Science Foundation (NSF) grants ATM-0215843 and INT-0110397; Portuguese
Foundation for Science and Technology (FCT) grants POCTI-32649-CTA-2000;
SFRH/BD/9049/2002; and Portuguese Regional Govern of Azores and especially
Professor Richard Honrath (1961–2009).

PYR: the framework of the UNEP – ABC (Atmospheric Brown Clouds) and EvK2CNR
– SHARE (Stations at High Altitude for Research on the Environment) projects
and the appreciated collaboration with the technical Nepalese staff.

SBO: TU Wien, Commission of Climate and Air Quality – ÖAW, Local
Government of Salzburg – Immissionsschutz, Umweltbundesamt GmbH and Aerosol
d.o.o.

SPL: Randolph Borys, Ian McCubbin, Douglas Lowenthal, Peter Atkins, and
Joe Messina, the US National Science Foundation (grant AGS-0079486), the
Steamboat Ski Resort and the Desert Research Institute, a permittee of the
Medicine–Bow Routt National Forests

TLL: Federal Office of Meteorology and Climatology MeteoSwiss through the
project Capacity Building and Twinning for Climate Observing Systems (CATCOS)
Phase 2, Contract no. 81025332 between the Swiss Agency for Development and
Cooperation and MeteoSwiss, Günther Wehrle from Paul Scherrer institute,
the site operator Luis Valle from DGAC and to the maintenance staff from
MeteoChile.

WLG: National Scientific Foundation of China (41675129), National Key Project
of MOST (2014CB441201) and the CMA Innovation Team for Haze-fog Observation
and Forecast.

High altitude stations are often emphasized as free tropospheric measuring sites but they remain influenced by atmospheric boundary layer. An ABL-TopoIndex is defined from a topography analysis around the stations. This new index allows ranking stations as a function of the ABL influence due to topography or help to choose a new site to sample FT. The ABL-TopoIndex is validated by aerosol optical properties and number concentration measured at 29 high altitude stations of five continents.

High altitude stations are often emphasized as free tropospheric measuring sites but they remain...